# Chemical Engineering by benbenzhou

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```									                           Chemical Engineering 301 0

Lecture Notes

Chapters 1-2. Introduction and First Law

Chapter 1. Introduction.

Syllabus. Pass out and discuss.

Web. Indicate location of syllabus and course materials on the World Wide Web
"courses" to this course).

Scope of Thermodynamics.

   relate changes in the equilibrium state of a system to interactions between the
system and its surroundings
   determine the efficiencies of alternative processes to effect a given change in
state, with respect to the resources available
   calculate equilibrium states for systems involving multiple phases and
chemical reactions
   measurement, estimation, and correlation of thermodynamic properties

Basic Relations.

First law:      E t  Q  W  E ( flow)  E ( gen)

Q
Second law:     S t          S ( flow)  S ( gen)
T

Phase equilibrium relations:     fi   fi       fi 

Chemical reaction equilibrium:
i
 fi 
 RT ln K  G   o
K   
 fi 

The Devil is in the Details.

   simplification of general thermodynamics relations to apply to a real, complex
problem
   combination of relations and setting up a solution scheme
   determination of relationships of internal energies, entropies, and fugacities to
measurable properties (T, P, composition, density, etc.) for real fluids and
solids
   understanding the use of thermodynamic tables, charts, and equations -
representing measured properties, theoretical estimations, and empirical
correlations
   estimation of the accuracy of the calculated results

First Assignments.

1. Get on the Web and find syllabus, information on teams, and class notes.
2. Read Chapters 1 and 2 in the text.

Basic Concepts.

A list of basic definitions can be found at the end of the syllabus.

Concepts which you should understand from previous courses:

   system
   surroundings
   system boundaries
   temperature
   pressure
   work
   heat
   material balance
   energy balance

Temperature - the property which tells us whether systems are in thermal equilibrium,
i.e., no heat transfer if two bodies at the same temperature are brought into thermal
contact.

Heat - energy in transition across the boundaries of a system due to a temperature
difference.

Work - energy in transition across the boundaries of a system due to a driving force other
than temperature, and not associated with mass flowing across the boundaries.

   Work in moving the system boundaries against an opposing pressure.

V 
dW   Fdl   PAd     PdV
 A
   Other types of work: shaft work, electrical work, surface spreading, etc.

Types of energy: kinetic, potential, internal.

mu 2
E t
 mgz  U t
2
State and path functions:

   Discuss intensive and extensive properties (t means total).
   State - unique set of intensive properties specifies the intensive state - the
extent of the system (total mass) must also be specified to completely specify
the overall state of a system.
   State functions - depend only on the state of a system, and not its past history -
such as U, H, S, etc. - when differential changes in state functions are
integrated over a finite accounting period, differences are obtained:
 dU  U 2  U 1 .
t     t     t

   Path functions - related to changes in the state of a system, and depend on how
these changes take place - such as Q, W, E(flow), E(gen), etc. - when
differential amounts of these functions are integrated over a finite accounting
period, total amounts are obtained:  dQ  Q .
   Process - change in the state of a system - cyclic processes return to the same
initial state.

Chapter 2. The First Law of Thermodynamics

General Differential Form (Differential Accounting Period).

dE t  dQ  dW  dE ( flow)  dE ( gen)

General Integrated Form (Finite Accounting Period).

E2  E1t  Q  W  E ( flow)  E ( gen)
t

Some simplifications:

steady-state: Et2 - Et1 = 0
closed system: E(flow) = 0
negligible kinetic and potential energies: Et = Ut
no reactions or other sources or sinks: E(gen) = 0
isolated system: Q, W, E(flow) = 0

Batch Process with No Generation.

This is a closed system, with negligible kinetic and potential energy changes.

U 2  U 1t  Q  W
t

U t  Q  W

Note that the change (the  on the left-hand side of this equation) is relative to
time, i.e., between the beginning and end of the accounting period.

Chemical reactions can be included in this equation by including U of reaction in
the Ut term.

If the batch process is carried out at constant pressure, then there will be a work
term.

W   PV t
H t  Q  Ws

where the shaft work term represents any other work that might be introduced.

Steady-State Flow Process with No Generation.

See Fig. 2.7, p. 52, as an example.

0  Q  W  E ( flow)
W  Ws  PV1  P2V2  Ws  PV
1

       mu 2      
E ( flow)  E 1  E 2   E     U t        mgz
        2        
       mu 2                           mu 2      
0  Q  Ws  PV    U t        mgz  Q  Ws    H t        mgz
        2                              2        

Rewriting, with the last term on the left-hand side, we get

 t mu 2      
 H      mgz  Q  Ws
     2       
Note that the change in this equation is between positions (cross sections 1 and 2),
rather than time.

If there is only one stream flowing in and one stream flowing out, this equation
can be written per unit mass of fluid flowing through the system:

     u2     
 H      gz  Q  Ws
     2      

where Q and Ws are the heat and shaft work per unit mass. This is Eq 2.32, p. 51.

In many applications, the kinetic and potential energy changes are small, and these
terms can be dropped from the LHS to get Eq 2.33 in the text.

General Form - Expanded.

E2  E1t  Q  W  E ( flow)  E ( gen)
t

 t mu2               mu2                         mu2                mu2      
U      mgz  U t       mgz  Q  Ws   H t       mgz   H t       mgz  E ( gen)
    2       2         2       1                   2        in        2        out

Work Example Problems.

Example Problem 2.16 on p. 54 - use as a group exercise:
1. What is the basis used by the author in applying the 1st law? What is
the accounting period?
2. gc is a units conversion factor. What are its units?
3. Where are the steam tables? Find the inlet and outlet conditions.
4. What would the final T be if Q=0?

Equilibrium.

   a state of absolute rest
   no tendency to change state
   no processes
   no fluxes of energy, mass, or momentum
   no temperature, pressure, or concentration gradients
   thermal, mechanical, and chemical equilibrium
   phase and chemical reation equilibrium
The Phase Rule.

phase - a homogeneous region with uniform intensive properties at equilibrium

- may be a liquid, vapor, or solid
- may be continuous or discontinuous (dispersed)

degrees of freedom (F) = number of intensive variables that must be specified to
fix the state of a system

phase equilibrium variables = T, P, compositions of all N components (in all 
phases)

Phase Rule (applies at equilibrium):

If there are no chemical reactions involved,

F  N  2 
If there are r independent chemical reactions at equilibrium (see p. 591),

F  N 2  r
Reversible Processes.

reversible process - can be reversed at any time by an infinitesimal change in the
driving force

Can you describe the following?

1. reversible expansion (work) in a piston and cylinder
2. reversible heat transfer between a solid and a bath

reversible work         dW   PdV

Reversible processes in closed systems - heat capacities.

U                   H
Definitions:     CV                 CP     
  T V              TP
1. Constant volume process.

dQ  dU t  ndU  nCV dT
T2

Q  U  nU  n  CV dT
t

T1

2. Constant pressure process.

dQ  dU t  PdV t  dU t  dPV t  dH t  ndH  nCP dT
T2

Q  H  nH  n  CP dT
t

T1

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